### Forecast

Dear Ms. Jones: In order to obtain the forecast for the fifth year we had to gather and analyze the data of the four previous years in your company. The trend (data behaving with the same frequency over the years) that was found was the following: The beginning months of the year are the ones with higher sales. As the months go by, sales continue decreasing until December, where sales come back up again. Now, let me explain how we were able to arrive to this conclusion. First, we calculated the average demand by adding up all the sales of all four years and dividing them by the number of months (48).

Then, we came up with the ratio by dividing the sales of each period by the average demand. The seasonal index is then obtained by getting the average of the same month ratios of all four years. For example, the average of all the 4 January ratios. The seasonal index is an average that can be used to compare an actual observation relative to what it would be if we there were no seasonal variation. We arrive to the seasonal forecast by dividing the sales by the seasonal index. Then we get the trend line by adding the intercept plus the x-variable and multiplying that by each period.

The trend forecast is what will show you the regular trend of the years. That is obtained by multiplying the trend line times the seasonal index. Here’s a snapshot of the trend of the what the fifth year would look like: And here is another graph showing the trend of the four previous years: As you can tell, the sales behavior repeats itself throughout the years. This trend seems to be very consistent. However, I must warn you that the p-value (percentage defective) in the summary output is significantly higher than . 06, (it is a. 404056) and this means this forecast is not very reliable.

I also calculated the percentage errors; the absolute percentage error (MAPE) is 3. 85%. This error was calculated by dividing the absolute error (which we got by subtracting the trend forecast from the sales and using the absolute value of that), by the sales, and then getting the percentage of all the absolute percentage errors. I hope this helps you understand the trend of your sales throughout a year. The most important thing for you to identify is the months where you are having higher sales the possible reasons why those sales decrease as the years comes to an end.